Question

An inductance $L$, resistance $R$, battery $B$ and switch $S$ are connected in series. Voltmeters $V_L$ and $V_R$ are connected across $L$ and $R$ respectively. When the switch is closed:

• A. The initial reading in $V_L$ will be greater than in $V_R$.
• B. The initial reading in $V_L$ will be less than $V_R$.
• C. The initial readings in $V_L$ and $V_R$ will be the same.
• D. The reading in $V_L$ will be decreasing with the increase in time.

Answer 1

Answer: (A), (D)

The reading in $V_L$ will be decreasing with the increase in time.

We know that an inductor behaves like an open circuit when the switch is just closed. Therefore, initially, all the voltage of the battery will drop across the inductor only.

Hence, the initial reading in $V_L$ will be greater than that in $V_R$.

With time, the current is built up in the circuit and therefore the voltage across the inductor will gradually decrease while the voltage across the resistor will gradually increase.

The variations of the $V_L$ and $V_R$ with time are shown below.


Hence, options $\left(\text{A}\right)$ and $\left(\text{D}\right)$ are the correct answers.